A new construction of the degree of maximal monotone maps

TL;DR

This paper introduces a simplified method for constructing the degree of maximal monotone maps between certain Banach spaces, facilitating easier calculations and classical theorem proofs in convex analysis.

Contribution

It presents a novel, simpler construction of the degree for maximal monotone maps in specific Banach space settings, improving upon classical methods.

Findings

Simplified degree construction for maximal monotone maps

Facilitates easier calculation of degree in nonlinear analysis

Proves classical convex analysis theorems using the new degree

Abstract

The inclusion equations of the type $f \in T ( x)$ where $T: X \to 2^{X^{\ast}}$ is a maximal monotone map, are extensively studied in nonlinear analysis. In this paper, we present a new construction of the degree of maximal monotone maps of the form $T: Y \to 2^{X^*}$, where $Y$ is a locally uniformly convex and separable Banach space continuously embedded in the uniformly convex Banach space $X$. The advantage of the new construction lies in the remarkable simplicity it offers for calculation of degree in comparison with the classical one suggested by F. Browder. We prove a few classical theorems in convex analysis through the suggested degree.